Passive micro-roughness array for drag modification

ABSTRACT

The present invention is directed to a micro-array surface that provides for either drag reduction or enhancement. In one aspect, an aerodynamic or hydrodynamic wall surface that is configured to modify a fluid boundary layer on the surface comprises at least one array of roughness elements disposed on and extending therefrom the surface. In one example, the interaction of the roughness elements with a turbulent boundary layer of the fluid reduces the skin friction drag coefficient of the surface over an identical smooth surface without the roughness elements.

This application claims priority to U.S. Provisional Application Nos.60/775,397, filed on Feb. 21, 2006, which is incorporated in itsentirety in this document by reference.

FIELD OF THE INVENTION

The present invention relates in general to an improved apparatus forreducing or enhancing the skin friction drag of an aerodynamic orhydrodynamic surface, and in particular to an improved micro-arraysurface design for reducing or enhancing the skin friction dragcoefficient and/or heat transfer rate of aerodynamic or hydrodynamicsurfaces.

BACKGROUND

The promise of drag reduction over solid surfaces in high Reynoldsnumber flows is one that has captured the attention of researchers foryears, yet has remained illusive. In the past, numerous approaches haveused both passive and active methods to control the flow in a turbulentboundary layer. In one exemplary approach, it is relatively well knownthat the aerodynamic drag of a surface may be reduced by applying amicroscopic “texture” to the otherwise smooth surface. Although theexact fluid dynamic mechanism at work in this drag reduction is not wellunderstood, it is speculated that the reduction relates to controllingthe turbulent vortices in the boundary layer adjacent to the surface.The microscopic texture reduces the skin friction drag of solids movingthrough fluids (e.g., aircraft, ships, cars, etc.), and of fluids movingalong solids (e.g., pipe flow, etc.).

One well known geometric form for a microscopic, friction-reducingtexture is known as “riblets.” Conventionally, riblets are positioned ona surface to form an integrated series of groove-like peaks and valleyswith V-shaped cross-sections. Normally, the riblets are positioned toextend along the aerodynamic surface of the object in the direction offluid flow. In one example, the height of the riblets and the spacingbetween the riblets are usually uniform and on the order of 0.001 to0.01 inches for most applications.

Dimensionless units, sometimes referred to as wall units, areconventionally utilized in describing fluid flows of this type. The wallunit h+ is the non-dimensional distance away from the wetted surface ormore precisely in the direction normal to the surface, extending intothe fluid. Thus h+ is a non-dimensional measurement of the height of theriblets. The wall unit s+ is the non-dimensional distance tangent to thelocal surface and perpendicular to the flow direction, thus thenon-dimensional distance between the riblets. In the prior art riblets,h+ and s+ are in the range between 10 and 20. Exemplary riblet designscan comprise an adhesive film applied to a smooth solid surface oralternatively, with advanced manufacturing techniques, the same shapesmay be directly formed and integrated into the structure of theaerodynamic surface.

The interaction of riblets with the structure of the turbulent boundarylayer of the fluid reduces the skin friction drag coefficient (Cdf) ofthe surface by approximately 6% compared to an identical smooth surfacewithout riblets. This reduction occurs despite the significant increasein “wetted area” (the surface area exposed to the fluid stream) of ariblet-covered surface over a smooth surface. In attempts to furtherreduce the Cdf, modifications to conventional V-shaped riblets have beenproposed. Examples include rounding of the peaks and/or valleys of therespective riblets, as well as even smaller V-shaped notches in thesides of the larger V-shaped riblets.

Further examples of improved riblet designs that decreases skin frictiondrag with less concomitant increase in wetted area than conventionalriblets include the use of a series of parallel riblets that extendlongitudinally from a smooth surface. In this example, the riblets havea triangular cross-section in the transverse direction in which the apexof the cross-section defines a continuous, undulated ridge with peaksand valleys that causes an effective reduction in Cdf. The wetted areaof this exemplary design is increased less than with conventionalriblets.

SUMMARY

Embodiments of this invention provide a surface of an object that isconfigured to provide for either drag reduction or enhancement, with thelatter being beneficial in applications where increased turbulent mixingis desired such as in heat transfer applications. In one aspect, anaerodynamic or hydrodynamic wall surface that is configured to modify afluid boundary layer on the surface comprises at least one array ofroughness elements disposed on and extending therefrom the surface. Inone example, the interaction of the roughness elements with a boundarylayer of fluid can act to delay transition to reduce the skin frictiondrag coefficient of the surface over an identical smooth surface withoutthe roughness elements.

Other systems, methods, features, and advantages of the passivemicro-array system will be or become apparent to one with skill in theart upon examination of the following figures and detailed description.It is intended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe passive micro-array system, and be protected by the accompanyingclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate certain aspects of the instantinvention and together with the description, serve to explain, withoutlimitation, the principles of the invention. Like reference charactersused therein indicate like parts throughout the several drawings.

FIG. 1 shows a schematic flow model for a drag enhancing d-type surfaceroughness, in which downwash is shown between the counter-rotatingvertex pair and upwash, that would occur on either side, is shown on thefront region of the surface roughness.

FIG. 2 shows a schematic flow model for a drag reducing d-type surfaceroughness, in which outflow, as depicted by the arrows, from theupstream cavity to the adjacent neighboring downstream cavity occursthrough the valleys in the saw tooth geometry of the formed ridges.

FIG. 3 shows a schematic front elevational view of one embodiment of aridge of an array of roughness elements of the present invention. In oneaspect, for drag reduction, the elements can be aligned such that thepeaks of the roughness elements of each adjacent ridge can be staggeredand can be spaced at about half the peak height of the roughnesselement. In this view, flow will encounter the ridge by moving into thefigure. In one exemplary aspect, the spacing between the peaks of theadjoined roughness elements is on the order of about 30 viscous lengthscales at close to maximum velocity for the fluid passing over the wallsurface.

FIG. 4 is a side elevational schematic view of the exemplary micro-arrayof roughness elements shown in FIG. 3, showing the tops of the roughnesselements of FIG. 3 and showing the formation of counter-rotatingstreamwise vortices due to the staggered alignment of adjacent rows ofthe roughness elements in the drag enhancing case. The flow of fluid isdirected into the figure.

FIG. 5 is a top elevational schematic view of exemplary vertexstructures that form within the transversely extending cavities of anexemplary micro-array of roughness elements of FIG. 3 of the presentinvention, showing fluid flow moving from the bottom to the top of thefigure and showing dark short lines correspond to the peaks of theroughness element in FIG. 3.

FIG. 6 is a perspective view of one embodiment of a roughness element ofa micro-array of the present invention, showing riblets formed on afront, upstream surface of the roughness element.

FIG. 7 is a side elevational view of the roughness element of FIG. 6.

FIG. 8 is a top elevational view of the roughness element of FIG. 6.

FIG. 9 is front, upstream elevational view of a plurality of adjoinedroughness elements of FIG. 6 that form a ridge, and showing a pluralityof channels formed between portions of the respective bases and thebottom portions of the peripheral edges of the respective adjoinedroughness elements.

FIG. 10 is a perspective view of a portion of a micro-array of thepresent invention, showing a plurality of staggered rows of the formedridges of adjoined roughness element of FIG. 8, and showing theapproximate spacing between the rows of ridges to be approximately halfthe height of a roughness element.

FIG. 11 is a schematic diagram of cavity flow of representative fluidflow between the tops of roughness elements of FIG. 6 and across one“valley,” the roughness elements being positioned in adjacent ridges orrows. In this diagram, fluid flow over the surface is from left toright.

FIG. 12 is a top elevational schematic view of exemplary vertexstructures that form on an exemplary micro-array of roughness elementsof FIG. 6 of the present invention, showing fluid flow moving from theleft to the right of the figure. The orange vortices represent the outervortices shown in FIG. 11 and may have small counter-rotating vorticessuperimposed on the outer-vortices that make the flow field consistentto its neighboring vortices. In the exemplified aspect with threeriblets on the front face of the roughness element, two counter-rotatingvortices would form with an upwelling between them and a downwash to theflow at the sides. These vortices are also known as Taylor-Gortlervortices. The blue vortex tubes represent the vortex cores to the vortexarray that link all the individual outer cavity vortices together.

FIG. 13 is a graphical illustration of a two-dimensional computationalfluid dynamics (CFD) numerical calculation through a line of symmetryover the peaks and valleys; of the roughness elements in drag reductionmode. The cavity Re for this calculation is 2000, and the formation ofstable cavity vortices is observed.

FIG. 14 is a graphical illustration of the velocity profiles in theboundary layer forming over the surface in FIG. 13 above the third andeighth cavities. These profiles are compared to that of a flat plateboundary layer, known as the Blasius solution. One can observe thenon-zero velocity over the surface of the cavities due to the embeddedcavity vortex. One skilled in the art will appreciate that one canobtain the momentum thickness of the two boundary layers, which isproportional to the total drag coefficient on the plate from the leadingedge to that corresponding downstream distance, by integrating thesevelocity profiles. In one example, the momentum thickness over the thirdcavity is 16.09% of the momentum thickness of the flat plate Blasiussolution, while at the eighth cavity the percentage of the momentumthickness of the surface with cavities with respect to the flat platesolution is 23.91%. Thus, at the third and eighth cavity, the dragcoefficient is reduced by 84% and 76% correspondingly.

DETAILED DESCRIPTION OF THE INVENTION

The present invention can be understood more readily by reference to thefollowing detailed description, examples, drawings, and claims, andtheir previous and following description. However, before the presentdevices, systems, and/or methods are disclosed and described, it is tobe understood that this invention is not limited to the specificdevices, systems, and/or methods disclosed unless otherwise specified,as such can, of course, vary. It is also to be understood that theterminology used herein is for the purpose of describing particularaspects only and is not intended to be limiting.

The following description of the invention is provided as an enablingteaching of the invention in its best, currently known embodiment. Tothis end, those skilled in the relevant art will recognize andappreciate that many changes can be made to the various aspects of theinvention described herein, while still obtaining the beneficial resultsof the present invention. It will also be apparent that some of thedesired benefits of the present invention can be obtained by selectingsome of the features of the present invention without utilizing otherfeatures. Accordingly, those who work in the art will recognize thatmany modifications and adaptations to the present invention are possibleand can even be desirable in certain circumstances and are a part of thepresent invention. Thus, the following description is provided asillustrative of the principles of the present invention and not inlimitation thereof.

As used in the specification and the appended claims, the singular forms“a,” “an” and “the” include plural referents unless the context clearlydictates otherwise. Thus, for example, reference to “a roughnesselement” includes arrays of two or more such roughness elements, and thelike.

Ranges can be expressed herein as from “about” one particular value,and/or to “about” another particular value. When such a range isexpressed, another embodiment includes from the one particular valueand/or to the other particular value. Similarly, when values areexpressed as approximations, by use of the antecedent “about,” it willbe understood that the particular value forms another embodiment. Itwill be further understood that the endpoints of each of the ranges aresignificant both in relation to the other endpoint, and independently ofthe other endpoint. It is also understood that there are a number ofvalues disclosed herein, and that each value is also herein disclosed as“about” that particular value in addition to the value itself. Forexample, if the value “10” is disclosed, then “about 10” is alsodisclosed. It is also understood that when a value is disclosed that“less than or equal to” the value, “greater than or equal to the value”and possible ranges between values are also disclosed, as appropriatelyunderstood by the skilled artisan. For example, if the value “10” isdisclosed the “less than or equal to 10” as well as “greater than orequal to 10” is also disclosed. It is also understood that throughoutthe application, data is provided in a number of different formats andthat this data represents endpoints and starting points, and ranges forany combination of the data points. For example, if a particular datapoint “10” and a particular data point 15 are disclosed, it isunderstood that greater than, greater than or equal to, less than, lessthan or equal to, and equal to 10 and 15 are considered disclosed aswell as between 10 and 15. It is also understood that each unit betweentwo particular units are also disclosed. For example, if 10 and 15 aredisclosed, then 11, 12, 13, and 14 are also disclosed.

As used herein, the terms “optional” or “optionally” mean that thesubsequently described event or circumstance may or may not occur, andthat the description includes instances where said event or circumstanceoccurs and instances where it does not.

The present invention may be understood more readily by reference to thefollowing detailed description of embodiments of the invention and theExamples included therein and to the Figures and their previous andfollowing description.

Referring to FIG. 1, an array of roughness elements 10 with the inducedflow field is illustrated. As shown, spanwise or transverse cavities 16defined between the ridges 12 that are exemplarily formed from adjoinedroughness elements 20 that are positioned substantially transverse tothe flow of the fluid over the surface 2, which results in a series ofcavity flows, each containing a re-circulating flow field. In theexemplary embodiment illustrated in FIGS. 1 and 2, roughness elements 20are integrally connected together to form individual ridges 16 that arepositioned on and extend from the surface 2 substantially transverse tothe flow of fluid across the surface 2. In one aspect, the ridges 16 arespaced substantially uniform and, optionally can be variably spaced.

In one aspect, due to the spacing of the saw tooth peaked roughnesselements 20, an on average streamwise vortex forms in the flow aboveeach cavity, such as found in the case of drag enhancing riblets. In oneaspect, it is contemplated that the cavities would comprise vortices ofalternating sign as this would appear to provide the most stable flowregime. In this aspect, and as illustrated, neighboring vorticescontribute to upwashes and downwashes in an alternating manner acrossthe spanwise direction.

One skilled in the art will also appreciate that alternative shapes ofthe roughness elements 20 are contemplated. Exemplary alternative shapescan comprise, but are not meant to be limited to, a blade-like thinpeak, which allows the formation of an increased number of vortices in apredetermined spanwise dimension, a trapezoidal cross-sectional shapewith a flat portion of the ridge over which the vortices will form, andthe like.

Independent of the ideal shape of the ridges 12, the overallcharacteristics of the flow field remains unchanged. In operation, andreferring to FIG. 1, a fluid particle would enter from the left at somedistance above the surface 2, such as exemplary shown as a flat plate.As the fluid particle approaches the surface it feels the presence moreof the counter-rotating vortex pair and is pulled downward into a regionof downwash. As it enters this downwash, the fluid particle enters' thecavity 16 and is spun around, in an almost slingshot type motion, andinjected back out above the surface through an upwash region of thechannels. From a heat transfer standpoint, the proposed surface causesfluid particles far away from the surface to come in contact (or verynear) to the surface for a short period of time and then to be pushedout again far above the surface. With this “on average” flow field, theburst/sweep process has been accentuated and controlled to take place inan organized manner. Thus, in one aspect, the exemplary array ofroughness elements 10 provides an efficient manner by which a turbulentboundary layer flow can be optimized for convective heating/coolingpurposes over a solid surface.

In one aspect of the invention, in order to cause as much fluid aspossible to come in contact with the “rough” surface 2, the spacingbetween the transverse cavities 16 should be minimized. However, if thespacing became too small, the mass flow rate pumped through the cavitieswould decrease due to viscous effects. In one exemplary aspect, theaverage height of the ridges (h⁺) is substantially equal to the width ofthe cavity (w⁺), or is about a one to one height to width ratio (h⁺≈w⁺).In another aspect, with respect to the average height of the cavities,it can be greater than about half the peak-to-peak amplitude of the sawtooth pattern along the ridges. In an exemplary aspect, the amplitudefor riblet spacing would be about and between 10s⁺ to 20s⁺. In anotherexample, the amplitude would be about 15s⁺. In this aspect, this wouldalso be the average height of the ridges, with the minimum valley pointof the ridges located at an elevation of s⁺ that is about 7.5 (±2.5)above the bottom of the cavity, and maximum peak located at s⁺ that isabout 22.5 (±2.5).

In a further aspect, the wavelength of the saw tooth pattern can beabout λ⁺=40, based on the size of a typical vortex mentioned previouslyof s⁺ being about 30. This would be sufficient to hold a vortex betweenthe peaks. Of course, it will be appreciated that these dimensions areexemplary only and are not meant to be limiting. Further, one willappreciate that the exemplary dimensions can be scaled as desired.

Referring now to FIG. 2, an exemplary flow field through the dragreducing roughness element 20 is illustrated. It has been demonstratedthat a series of transverse cavities 16 with substantially constantridge height is prone to a random efflux/influx of fluid due to the highshear region located above the cavities. This high shear region resultsin the formation of streamwise vortices and low speed streaks above thecavities such as found in the smooth surface case. It is likely that thepeak velocity may be larger for cavities 16 formed by a series oftransverse blades, but would more than likely still be a large enoughpercentage below the freestream that streamwise vortices would still beformed due to a high shear region above the cavities. As shown in FIG.2, to prevent and/or reduce the efflux/influx process out/into thecavities, a saw tooth geometry is defined by the respective roughnesselements 20 that form the ridges of the array of roughness elements.

In this example, the substantially transverse cavities formed betweenthe adjacent ridges help with the stability of the flow field as theflow through the cavities is given a longer distance (two cavity widthsas opposed to one) by which it is exposed and pulled along by the flowdirectly above. As a result of the exemplary geometry, the estimatedpeak velocity achieved is in a range between about 5 to 40 percent ofthe freestream flow. Second, the jets formed through the cavities aresubstantially tangent to the flow above so that very little verticalvelocity component is formed. If one were looking down onto the surface,the formed jets would appear to be a periodic array of suction andblowing at a smooth wall. Finally, the flow acting on the bottom of thecavities results in a shear stress that provides thrust to the surface.In this case the effect is such that it may act to cancel out a largepercentage of the skin friction losses due to the momentum change in theflow over the vertical walls of the cavities. It is contemplated thatthis effect is more pronounced as higher peak velocities in the jets(and thus closer to the bottom surface of the cavities) are achieved.Thus, in one example, the width of the cavities 16 can be increased ormaximized (such that the stable flow field in FIG. 2 is maintained) soas to decrease the number of spanwise channels over a given surfacearea.

In this aspect, considering an averaged streamline through the roughnesselement, a fluid particle that starts from the left close to the surfacewould approach a transverse cavity in the array and upon entering thecavity be captured by the cavity vortex and travel around in a spiralmotion before being passed through another cavity just to enter theneighboring cavity and repeat the previous motion. In this example, allfluid near the ridge stays near the ridge and there is little or no onaverage vertical velocity component away from the cavities of the array.Given the flow model as stated, and that the cavities are dimensionallysmall enough such that viscous effects dominate, it is contemplated thatthe net skin friction drag over such an exemplary surface could start toapproach that of a laminar flat plate boundary layer.

In one aspect, the formed “rough” surface can be categorized as a seriesof trapezoidal channels (d-type roughness geometry) that are orientatedin the spanwise direction (transverse to the flow of fluid across thearray), but, in one exemplary aspect, with a saw tooth geometry ofalternating peaks along the ridges of the channels giving the surface athree-dimensional, yet repeatable, pattern. The alignment of the peaksin the streamwise direction of the flow of fluid is proposed to increasedrag, while the alternation of the peaks in the streamwise directionwill decrease drag. In one aspect, the spacing between the ridges in thestreamwise direction can vary from ½ to a full value of the peak height(or amplitude) of the ridges with respect to the bottom of the cavities.In another aspect, the distance between adjacent successive ridges canbe in a range of between about 40 to 60% of the peak longitudinal heightor amplitude of the roughness elements that form the respective ridges.Optionally, the distance between adjacent successive ridges can be in arange of between about 45 to 55% of the peak longitudinal height oramplitude of the roughness elements that form the respective ridges

In an alternative embodiment of the invention, and referring now toFIGS. 3-12, the micro-array 10 can comprise a plurality of roughnesselements 20 that can extend from the surface and be positioned in spacedridges 16 along the surface 2. In this aspect, it is contemplated thateach roughness element 20 has a front, upstream surface 22 and anopposing rear, downstream surface 24. Further, each roughness elementhas a peripheral edge 26 that has an upper portion 28 that tapers to atop 29 and a bottom portion 30 that tapers to a base 31. As one wouldappreciate, the base is configured to be connected to the underlingsurface 2 of the object. In one exemplified aspect, the roughnesselements 20 are positioned on the underlying surface 2 substantiallytransverse to the flow of the fluid across the surface. In anotheraspect, the roughness elements extend substantially normal to theunderlying surface. For example, and not meant to be limiting, thetransverse longitudinal height of the roughness elements can be betweenabout 0.001 to 2.00 cm.

In one aspect of the invention, a plurality of roughness elements 20 canbe positioned transverse to the flow of fluid across the surface suchthat a distance between a medial portion 32 of the peripheral edges ofadjacent and aligned roughness elements 20 is less than the distancebetween the respective tops 29 of the roughness elements and is lessthan the distance between the respective bases 31 of the roughnesselements. In a further aspect of the inventions, adjacent and alignedroughness elements can be connected at some selected portion of therespective peripheral edges of the roughness elements. In this aspect, achannel 34 is defined therebetween portions of the bases and the bottomportions of the peripheral edges of the adjacent and adjoined roughnesselements. In one exemplary aspect, it is contemplated that the formedchannels would extend longitudinally substantially co-axial to the flowof the fluid across the surface. In an alternative aspect of theinvention, the adjoining roughness elements can be connected togethersuch that no channel is formed therebetween the respective adjoiningelements. In a further aspect, the adjoined roughness elements can forma “saw tooth” ridge that extends substantially transverse to the fluidflow.

In one embodiment, the roughness element 20 has a substantially diamondcross-sectional shape, as shown in FIG. 3. Alternatively, and as shownin FIG. 6, the roughness element 20 can have a substantially oval shape.Of course, one skilled in the art will appreciate that other geometricshapes are contemplated and that the aspects illustrated are merelyexemplary.

Referring now to FIGS. 6-10, in one aspect, it is contemplated that thefront, upstream surface 22 of the roughness element 20 has a curved,convex cross-sectional shape relative to the flow of fluid across thesurface 2 of the object. In another aspect, it is contemplated that therear, downstream surface 24 of the roughness element has a curved,concave cross-sectional shape relative to the flow of fluid to promotethe recirculation of the flow within the cavity, and to act as astreamlining effect in both stabilizing and promoting the embeddedvortex flow field. In one aspect, this slight concavity in the rearsurface 24 of the roughness element also acts to position the tops 29 ofthe roughness elements at a slight, acute angle relative to theunderlying surface such that the tops of the roughness elements do notprotrude into the fluid flow normal to the flow direction. In oneaspect, it is contemplated that the radius of curvature of the rearsurface 24 of the roughness element is less than the radius of curvatureof the front surface 22 of the roughness element.

In a further aspect of the present invention, each roughness element 20can have at least one riblet 40 extending outwardly therefrom the frontsurface 22 of the roughness element. In one aspect, the riblet 40extends longitudinally from at or near the bottom portion 30 of theroughness element, proximate the base 31, to at or near the top 29 ofthe roughness element. That is, in one aspect, the riblet extendssubstantially transverse to the underlying surface. If a plurality ofriblets are used, it is contemplated that the ribs can be spaced apartsubstantially equal or at varying distances. Of course, the number ofriblets 40 may vary in number, but typical values would be that from 1to 7 per each longer wavelength of the saw tooth pattern of the formedridge of the micro-array. In one aspect, the number of riblets is 1, 3,5, or 7.

The presence of the riblets 40 formed to either the front surface 22,or, optionally, to both sides of the roughness element, act to give astreamlining effect that is conductive to the formation and stability ofthe cavity flows (or vortices) embedded within the cavities formedbetween adjacent ridges or rows of the roughness elements. In oneaspect, the addition of the riblets to the roughness elementsmicro-geometry help to increase drag reduction, such as, for example,with higher speed flows. In a further aspect, the riblets 40 act toexcite counter-rotating vortices within the outer vortex structure thatwhen in even numbers (formed by an odd number of riblets) promote thestability of the vortex array in the surface.

Further, in another aspect, it is contemplated that a trough 42 isdefined therebetween adjacent riblets 40 that is recessed from therespective tips 44 of the riblets. In one aspect, the trough may beformed by a smooth, curved surface. Of course, it is contemplated thatthe surface of each of the troughs in the respective roughness elementcan have a substantially equal radius of curvature or can vary asdesired.

In another aspect, the riblets 40 have an edge surface 46 that extendsbetween the respective riblets that are adjacent to the sides of theroughness element. In one aspect, the edge surface 46 can besubstantially planar. Alternatively, at least a portion of the edgesurface can be curved. In the curved aspect, it is contemplated that theradius of curvature of the edge surface can be greater than the radiusof curvature of the troughs 42 of the roughness elements.

It is further contemplated that the geometry of the formed surface ofthe present invention can be altered as a function of the thickness ofthe boundary layer adjacent to the surface. For example, in regionswhere the boundary layer is thicker, the tops 29 of the roughnesselements 20 may also comprise an additional saw tooth pattern of shorterwavelength superimposed on the larger wavelength saw tooth pattern. Thisis of importance in regions far downstream from the leading edge of abody where the boundary layer is thicker, yet the flow outside theboundary layer and above the surface is of high velocity.

In a drag reduction mode, the saw tooth pattern on the tops 29 of theroughness elements 20 acts to inhibit the formation of the optimalperturbations that appear due to the instability of the shear flow (orboundary layer) above the roughness element and inside the boundarylayer. At lower speeds this wavelength is larger. Conversely, at higherspeeds this wavelength is smaller. In one exemplary aspect, the smallerwavelength superimposed on the larger saw tooth tops can vary frombetween about ⅓ to 1/7 that of the larger wavelength. The sizing is afunction of the speed of the flow outside the boundary layer adjacent tothe surface (U), the kinematic viscosity of the fluid (ν) and themaximum shear in the boundary layer ((du/dy)_(max)). It should be notedthat as a body moves at higher speeds, the boundary layer at aparticular point on the body will reduce in thickness and the maximumshear sustained in the boundary layer will increase. This corresponds toa decrease in the wavelength sizing required of the roughness element toact in drag reduction mode.

Regardless of whether a surface results in the formation of embeddedvortices within the respective roughness elements or not, the “maleprotrusions” that result from the roughness elements and their sizingmay be sufficient enough to delay the transition to turbulence in theboundary layer and thus still result in drag reduction. However, tomaximize the drag reduction characteristic of the micro-array ofroughness elements of the present invention would include both theformation of the embedded spanwise vortex array within the roughnesselement as well as the protrusion geometry of the roughness geometry,which leads to the damping of instabilities in the boundary layer thatresult in the transition to turbulence.

In addition, and as noted above, the downstream side of the roughnesselements can, or can not, comprise a slightly concavity to the surface(see FIG. 7) as well. This thickness to the peak of the formed ridgeprovides a smooth line of reattachment for the separated shear layerover the top of the cavity from the previous upstream roughness elementand at the top of the roughness element provides for a tangentialmeeting of this outer flow with the next downstream embedded cavityvortex (again, see FIG. 7). All of the elements listed here have to dowith the effects of streamlining the micro-geometry to promote theformation of a stable, embedded cavity vortex within the roughnesselement.

Further, it is contemplated that the micro-array of roughness elements10 on the surface 2 can comprise a plurality of micro-arrays ofroughness elements 10 on the respective surface 2. In this aspect, eachmicro-array can comprise a plurality of roughness elements, as describedabove, of a predetermined height and/or shape. Thus, it is contemplatedthat, the plurality of micro-arrays could comprise arrays of varyingsized or shaped roughness elements.

In another aspect, each micro-array of roughness elements can comprisesindividual roughness elements that vary in respective scale and/orshape. For example and not meant to be limiting, adjacent roughnesselement could have different relative scaled dimensions. Thus, a “large”roughness element can adjoin a “small” roughness element, such that afront view would be of a line or ridge of the adjoining roughnesselements that have a staggered saw tooth appearance.

In the arrays discussed above, the formed channel 34 between adjoiningroughness elements 20 allows for some of the reversed flow at the bottomof the cavities between adjacent span-wise extending ridges of lines ofthe roughness elements to head back upstream to the adjacent,neighboring cavity through the channels between the roughness elements.In operation, a cavity flow may result such that fluid particles stay inthe cavities to continue the circulatory pattern between the twocavities, i.e., entering the downstream cavity over the top of thevalley to return back to the upstream cavity through the gap beneath thevalley as shown in FIG. 11. The juncture of the two adjoining roughnesselements acts as a center for each individual cavity vortex and may alsoallow for a secondary pair of vortices to form inside the larger cavityvortex, which is also shown in FIG. 11. Referring to FIG. 12, thesevortices, one inside each transverse half cavity, provides a means ofinterlocking all of the cavity flows together in an almost chain-linktype array of streamlines that are relatively stable and are not subjectto cavity influx/efflux of flow, which leads to an increase in drag forthe d-type surface. As noted above, the micro-geometrical patterning ofa surface in this invention for maximum drag reduction mode results inthe formation of an array of embedded cavity flows (or vortices) betweenthe roughness elements.

It is contemplated that the flow arranged by this roughness element is aseries of micro-slip walls in which the orange ovals in FIG. 12 denoteeach micro-slip wall. From another standpoint, it is contemplated thatthe roughness element of the present invention alters the no slipcondition which the outside flow sees at the wall. Further, it is knownthat embedded cavity flow can be used as a means of separation controldue to the alteration of the no-slip condition at the surface. It iscontemplated that the roughness element described herein can be used inapplications that would reduce the pressure drag associated withseparated flows over surfaces.

In a further aspect of the “roughness” surface, the thickness of theboundary layer can be in a range of at least 10 to 30% of a cavityheight of each cavity such that shear layer instabilities of cavityvortexes that form therein the plurality of cavities are reduced.Preferably, about at least 20% of the cavity height. Typically, cavityheight would be measured from the surface 2 of the object to the peak orhighest amplitude of the roughness elements that form the transverselydisposed ridge. In one aspect, each formed cavity vortex can have a Re,relative to the cavity height, velocity of the fluid over the wallsurface, and the kinematic viscosity of the fluid, in the range ofbetween 100 and 20,000, such that the instability of the formed cavityvortexes are suppressed. Optionally, each formed cavity vortex can havea Re, relative to the cavity height, velocity of the fluid over the wallsurface, and the kinematic viscosity of the fluid, in the range ofbetween 1,000 and 5,000.

The micro-arrays of the roughness elements of the present inventionwould find applicability in drag reduction modalities, such as, forexample and not meant to be limiting, on the surfaces of aircraft,submarines, ship hulls, high speed trains and the like. In the case ofthe flow over the hull of a ship, the micro-arrays of the roughnesselements can impact the boundary layer formation over the hull andtherefore affect the amount of air ingested below the water line,thereby altering the entire flow field of a ship's wake. It is alsocontemplated than the micro-arrays can be used in pipeline walls aswell, which would result in a large reduction in the amount of energysaved to pump fluids from one point to another.

It is also contemplated that the micro-arrays of the present inventionallows for the trapping of pockets of air inside the cavities such that,for example, in hydrodynamic applications, the working fluid for themicro-slip walls would consist of these air pockets. This would alsoreduce the skin friction for hydrodynamic applications and, in anotheraspect, can reduce cativation.

Still further, the micro-arrays of roughness element can act as a meansof controlling separation. The effect of the arrays acts to reducepressure drag over bluff bodies such as automobiles and trucks. It canalso minimize separation over turbine blades, airfoils, and helicopterrotors as well as flow through serpentine ducts, which is often arequirement for inlet geometries for engines on an aircraft. Optionally,in a drag enhancement mode, a surface formed with the micro-array ofroughness elements of the present invention allows for highly effectiveconvective cooling to the surfaces of computer board components, whichcould greatly impact the performance of these devices.

It is also contemplated that the self-cleaning property of the roughnesselements should be excellent due to the high shear rates resulting overthe major portions of the surfaces of the roughness elements. However,it is also contemplated to use hydrophobic materials in constructing theroughness elements for hydrodynamic applications.

It is contemplated that a surface formed with a micro-array of roughnesselement as described above, could be formed for a saw tooth wavelengththat corresponds to that of the optimal perturbation wavelength for theshear flow inside the boundary layer. In this example, the alignment oralternation of the peaks to achieve maximum heat transfer rates andmaximum drag at a surface is considered. In one aspect, the alternationof the peaks forces the half-wavelength of the saw tooth amplitude tocorrespond to the optimal perturbation wavelength. Thus, it iscontemplated that the formed drag reducing surface could become dragenhancing as the flow speed is increased.

The preceding description of the invention is provided as an enablingteaching of the invention in its best, currently known embodiment. Tothis end, those skilled in the relevant art will recognize andappreciate that many changes can be made to the various aspects of theinvention described herein, while still obtaining the beneficial resultsof the present invention. It will also be apparent that some of thedesired benefits of the present invention can be obtained by selectingsome of the features of the present invention without utilizing otherfeatures. The corresponding structures, materials, acts, and equivalentsof all means or step plus function elements in the claims below areintended to include any structure, material, or acts for performing thefunctions in combination with other claimed elements as specificallyclaimed.

Accordingly, those who work in the art will recognize that manymodifications and adaptations to the present invention are possible andcan even be desirable in certain circumstances and are a part of thepresent invention. Other embodiments of the invention will be apparentto those skilled in the art from consideration of the specification andpractice of the invention disclosed herein. Thus, the precedingdescription is provided as illustrative of the principles of the presentinvention and not in limitation thereof. It is intended that thespecification and examples be considered as exemplary only, with a truescope and spirit of the invention being indicated by the followingclaims.

REFERENCES

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1. An aerodynamic or hydrodynamic wall surface configured to modify theinteraction of a boundary layer of a fluid with the wall surface,comprising: at least one array of roughness elements disposed on andextending therefrom the surface, wherein each roughness element has afront, upstream surface and an opposing rear, downstream surface,wherein each roughness element has a peripheral edge that has an upperportion that tapers to a top and a bottom portion that tapers to a base,which is connected to the wall surface, wherein a plurality of roughnesselements are positioned substantially transverse to the flow of fluidacross the surface such that a distance between a medial portion of theperipheral edges of adjacent and aligned roughness elements is less thanthe distance between the respective tops of the roughness elements andis less than the distance between the respective bases of the roughnesselements, wherein the array of roughness elements defines a plurality ofcavities, and wherein the thickness of the boundary layer is at least20% of a cavity height of each cavity such that shear layerinstabilities of cavity vortexes that form therein the plurality ofcavities are reduced.
 2. The wall surface of claim 1, wherein eachformed cavity vortex has a Re, relative to the cavity height, velocityof the fluid over the wall surface, and the kinematic viscosity of thefluid, in the range of between 100 and 20,000, such that the instabilityof the formed cavity vortexes are suppressed.
 3. The wall surface ofclaim 1, wherein each formed cavity vortex has a Re, relative to thecavity height, velocity of the fluid over the wall surface, and thekinematic viscosity of the fluid, in the range of between 1,000 and5,000, such that the instability of the formed cavity vortexes aresuppressed.
 4. The wall surface of claim 1, wherein the roughnesselements are positioned substantially transverse to the flow of thefluid across the wall surface.
 5. The wall surface of claim 6, whereinthe roughness elements extend substantially normal to the underlyingsurface.
 6. The wall surface of claim 1, wherein a transverselongitudinal height of the roughness elements can range between about0.001 to 2.00 cm.
 7. The wall surface of claim 4, wherein the array ofroughness elements are positioned in successive ridges of roughnesselements, wherein each ridge of roughness elements is positionedsubstantially transverse to the flow of fluid across the wall surface,and wherein each ridge of roughness elements forms a substantially sawtooth pattern of roughness elements having a selected wavelength.
 8. Thewall surface of claim 7, wherein one cavity of the plurality of cavitiesis formed between adjacent successive ridges of roughness elements. 9.The wall surface of claim 8, wherein the distance between adjacentsuccessive ridges is in a range between about 40 to 60% of the peaklongitudinal height of the roughness elements.
 10. The wall surface ofclaim 7, wherein the distance between adjacent successive ridges is in arange between about 45 to 55% of the peak longitudinal height of theroughness elements.
 11. The wall surface of claim 7, wherein a portionof the respective peripheral edges of the adjacent and aligned roughnesselements in a ridge of roughness elements are connected and define achannel between portions of the bases and the bottom portions of theperipheral edges of the adjacent and adjoined roughness elements. 12.The wall surface of claim 11, wherein each channel extendslongitudinally substantially co-axial to the flow of the fluid acrossthe wall surface.
 13. The wall surface of claim 7, wherein eachroughness element has a substantially diamond cross-sectional shaperelative to a plane transverse to the flow of fluid over the wallsurface.
 14. The wall surface of claim 7, wherein each roughness elementcan have a substantially oval cross-sectional shape relative to a planetransverse to the flow of fluid over the wall surface.
 15. The wallsurface of claim 7, wherein each roughness element has a front, upstreamsurface and an opposed, downstream surface, and wherein the front,upstream surface of each roughness element has a curved, convexcross-sectional shape relative to the flow of fluid across the wallsurface.
 16. The wall surface of claim 15, wherein the rear, downstreamsurface of each roughness element has a curved, concave cross-sectionalshape relative to the flow of fluid that is configured to promote therecirculation of the flow within the cavity and to act as a streamliningeffect in both stabilizing and promoting an embedded vortex flow field.17. The wall surface of claim 16, wherein the top of each roughnesselement is positioned at an acute angle relative to the wall surfacesuch that the tops of the roughness elements do not protrude into thefluid flow substantially normal to the flow direction.
 18. The wallsurface of claim 16, wherein a radius of curvature of the rear,downstream surface of the roughness element is less than a radius ofcurvature of the front, upstream surface of the roughness element. 19.The wall surface of claim 16, wherein each roughness element comprisesat least one riblet extending outwardly therefrom the front, upstreamsurface of the roughness element that is configured to aid in theformation and stability of cavity flows embedded between the roughnesselements.
 20. The wall surface of claim 19, wherein each riblet extendslongitudinally from at or near the bottom portion of the roughnesselement, proximate the base, to at or near the top of the roughnesselement.
 21. The wall surface of claim 20, wherein each riblet extendssubstantially transverse to the wall surface.
 22. The wall surface ofclaim 20, wherein the at least one riblet comprises a plurality ofriblets.
 23. The wall surface of claim 20, wherein the number of ribletsis in a range of between about 1 to 7 per each longer wavelength of thesaw tooth pattern of the formed ridge of the array.
 24. The wall surfaceof claim 19, wherein each roughness element comprises at least oneriblet extending outwardly therefrom the rear, downstream surface of theroughness element, and wherein each riblet extends substantiallylongitudinally.
 25. The wall surface of claim 22, wherein a trough isdefined therebetween adjacent riblets that are recessed from therespective tips of the riblets.
 26. The wall surface of claim 25,wherein the front, upstream portion of each roughness element has anedge surface that extends between respective riblets that are positionedadjacent to the sides of the roughness element.
 27. The wall surface ofclaim 26, wherein the edge surface can be substantially planar.
 28. Thewall surface of claim 26, wherein at least a portion of the edge surfacecan be curved, and wherein a radius of curvature of the edge surface isgreater than a radius of curvature of the trough of the roughnesselement.
 29. The wall surface of claim 24, wherein the top of eachroughness element comprises a saw tooth pattern of shorter wavelengthsuperimposed on the larger wavelength saw tooth pattern of the formedridge of roughness elements such that the formation of optimalperturbations are inhibited due to the instability of the shear flow orboundary layer of the fluid above the roughness element and inside theboundary layer.
 30. The wall surface of claim 29, wherein the smallerwavelength superimposed on the larger saw tooth tops can be in a rangeof from between about ⅓ to 1/7 that of the larger wavelength.
 31. Thewall surface of claim 7, wherein the roughness elements in adjacentridges of the array are positioned offset from each other relative tothe flow of fluid across the surface.
 32. The wall surface of claim 7,wherein each ridge of roughness elements of the array has a saw toothwavelength that is substantially equal to an optimal perturbationwavelength for the shear flow inside the boundary layer.
 33. The wallsurface of claim 1, wherein adjacent roughness elements within a ridgeof roughness elements can have different scaled dimensions, such thatthe formed ridge has a staggered saw tooth appearance.
 34. The wallsurface of claim 1, further comprising a means of interlocking aplurality of formed cavity flows, formed between the respectiveroughness elements, together in a substantially chain-link type array ofstreamlines that are relatively stable.
 35. An aerodynamic orhydrodynamic wall surface configured to modify the interaction of aboundary layer of a fluid with the wall surface, comprising: at leastone array of roughness elements disposed on and extending therefrom thesurface, wherein the array of roughness elements are positioned insuccessive ridges of roughness elements, wherein each ridge of roughnesselements is positioned substantially transverse to the flow of fluidacross the wall surface, wherein each ridge of roughness elements formsa substantially saw tooth pattern having a selected wavelength, whereineach roughness element has a peripheral edge, wherein adjacent andaligned roughness elements in a ridge of roughness elements areconnected at a medial portion of the respective peripheral edges of theroughness elements and define a channel between portions of the basesand the bottom portions of the peripheral edges of the adjacent andadjoined roughness elements, wherein the array of roughness elementsdefines a plurality of cavities, and wherein the thickness of theboundary layer is at least 20% of a cavity height of each cavity suchthat shear layer instabilities of cavity vortexes that form therein theplurality of cavities are reduced.
 36. The wall surface of claim 35,wherein each formed cavity vortex has a Re, relative to the cavityheight, velocity of the fluid over the wall surface, and the kinematicviscosity of the fluid, in the range of between 100 and 20,000, suchthat the instability of the formed cavity vortexes are suppressed. 37.The wall surface of claim 35, wherein each formed cavity vortex has aRe, relative to the cavity height, velocity of the fluid over the wallsurface, and the kinematic viscosity of the fluid, in the range ofbetween 1,000 and 5,000, such that the instability of the formed cavityvortexes are suppressed.
 38. The wall surface of claim 35, wherein eachchannel extends longitudinally substantially co-axial to the flow of thefluid across the wall surface.
 39. The wall surface of claim 38, whereinthe peripheral edge of each roughness element has an upper portion thattapers to a top and a bottom portion that tapers to a base, which isconnected to the wall surface, wherein a plurality of roughness elementswithin each ridge of roughness elements are positioned transverse to theflow of fluid across the surface such that a distance between themidpoints of the peripheral edges of adjacent and aligned roughnesselements is less than the distance between the respective tops of theroughness elements and is less than the distance between the respectivebases of the roughness elements.
 40. The wall surface of claim 25,wherein the array of roughness elements are positioned in successiveridges of roughness elements, wherein each ridge of roughness elementsis positioned substantially transverse to the flow of fluid across thewall surface, wherein each ridge of roughness elements forms asubstantially saw tooth pattern of roughness elements having a selectedwavelength, wherein one cavity of the plurality of cavities is formedbetween adjacent successive ridges of roughness elements, and whereinthe distance between adjacent successive ridges is in a range betweenabout 40 to 60% of the longitudinal height of the roughness elements.